Rings, Modules, and Closure Operations

This book presents a systematic exposition of the various applications of closure operations in commutative and noncommutative algebra. In addition to further advancing multiplicative ideal theory, the book opens doors to the various uses of closure operations in the study of rings and modules, with emphasis on commutative rings and ideals. Several examples, counterexamples, and exercises further enrich the discussion and lend additional flexibility to the way in which the book is used, i.e., monograph or textbook for advanced topics courses.

Auteur

Jesse Elliott is a professor of mathematics and philosophy at California State University Channel Islands. He received a PhD in Mathematics in 2003 from the University of California, Berkeley and received a BS in Mathematics in 1995 from the Massachusetts Institute of Technology. His areas of research are ring theory, number theory, and the philosophy of mathematics.

Contenu

Preface.- 0. Preliminaries.- 1. Introductory survey of multiplicative ideal theory.- 2. Semistar operations on commutative rings.- 3. Semistar operations on commutative rings: local methods.- 4. Extensions of commutative rings.- 5. Semiprime, star, and semistar operations on commutative rings.- 6. Closure operations on submodules over noncommutative rings.- 7. Appendix on Clusure operations and nuclei.- Bibliography.- Index.